{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SZX422USX5DZSGVNHYII5JH5N6","short_pith_number":"pith:SZX422US","schema_version":"1.0","canonical_sha256":"966fcd6a92bf47991aad3e108ea4fd6f9d99b9012c908ada3fb505c5f0853bdb","source":{"kind":"arxiv","id":"1108.4140","version":3},"attestation_state":"computed","paper":{"title":"Tiling 3-uniform hypergraphs with K_4^3-2e","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Czygrinow, Brendan Nagle, Louis DeBiasio","submitted_at":"2011-08-20T19:11:31Z","abstract_excerpt":"Let K_4^3-2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n, K_4^3-2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree \\delta_2(G) \\geq d contains \\floor{n/4} vertex-disjoint copies of K_4^3-2e. K\\\"uhn and Osthus proved that t(n, K_4^3-2e) = (1 + o(1))n/4 holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, t(n, K_4^3-2e) = n/4 when n/4 is odd, and t(n, K_4^3-2e) = n/4+1 when n/4 is even.\n  A main ingredient in our proof is th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.4140","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-20T19:11:31Z","cross_cats_sorted":[],"title_canon_sha256":"ad3319846e5ec7839a5829589b71008f2f96eee873f21b0ed8dae41d55eccf4c","abstract_canon_sha256":"96535840fb98ac99643e6219077c6f1c21940c596ec26d24b7d0c4961ffda4d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:46.398418Z","signature_b64":"ZKiaNHNATmlDoRj3Km4BTb1DQ0sAzCWBs7KDofjJWZyootSUg6vCLtUSK2aPGvV2N8nJpAjYtzFt9FBgWJctCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"966fcd6a92bf47991aad3e108ea4fd6f9d99b9012c908ada3fb505c5f0853bdb","last_reissued_at":"2026-05-18T03:38:46.397630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:46.397630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tiling 3-uniform hypergraphs with K_4^3-2e","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Czygrinow, Brendan Nagle, Louis DeBiasio","submitted_at":"2011-08-20T19:11:31Z","abstract_excerpt":"Let K_4^3-2e denote the hypergraph consisting of two triples on four points. For an integer n, let t(n, K_4^3-2e) denote the smallest integer d so that every 3-uniform hypergraph G of order n with minimum pair-degree \\delta_2(G) \\geq d contains \\floor{n/4} vertex-disjoint copies of K_4^3-2e. K\\\"uhn and Osthus proved that t(n, K_4^3-2e) = (1 + o(1))n/4 holds for large integers n. Here, we prove the exact counterpart, that for all sufficiently large integers n divisible by 4, t(n, K_4^3-2e) = n/4 when n/4 is odd, and t(n, K_4^3-2e) = n/4+1 when n/4 is even.\n  A main ingredient in our proof is th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4140","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.4140","created_at":"2026-05-18T03:38:46.397746+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.4140v3","created_at":"2026-05-18T03:38:46.397746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4140","created_at":"2026-05-18T03:38:46.397746+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZX422USX5DZ","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZX422USX5DZSGVN","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZX422US","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6","json":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6.json","graph_json":"https://pith.science/api/pith-number/SZX422USX5DZSGVNHYII5JH5N6/graph.json","events_json":"https://pith.science/api/pith-number/SZX422USX5DZSGVNHYII5JH5N6/events.json","paper":"https://pith.science/paper/SZX422US"},"agent_actions":{"view_html":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6","download_json":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6.json","view_paper":"https://pith.science/paper/SZX422US","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.4140&json=true","fetch_graph":"https://pith.science/api/pith-number/SZX422USX5DZSGVNHYII5JH5N6/graph.json","fetch_events":"https://pith.science/api/pith-number/SZX422USX5DZSGVNHYII5JH5N6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6/action/storage_attestation","attest_author":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6/action/author_attestation","sign_citation":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6/action/citation_signature","submit_replication":"https://pith.science/pith/SZX422USX5DZSGVNHYII5JH5N6/action/replication_record"}},"created_at":"2026-05-18T03:38:46.397746+00:00","updated_at":"2026-05-18T03:38:46.397746+00:00"}